#840515 (C++23) No.2013 Can we meet?

提出ソース
結果

問題	No.2013 Can we meet?
ユーザー	👑 emthrm
提出日時	2023-02-17 02:24:48
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	MLE
実行時間	-
コード長	21,145 bytes
コンパイル時間	4,591 ms
コンパイル使用メモリ	274,168 KB
実行使用メモリ	814,528 KB
最終ジャッジ日時	2023-09-26 05:37:01
合計ジャッジ時間	10,546 ms
ジャッジサーバーID （参考情報）	judge13 / judge11
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 4,380 KB
testcase_01	AC	2 ms 4,384 KB
testcase_02	AC	2 ms 4,384 KB
testcase_03	AC	2 ms 4,384 KB
testcase_04	AC	1 ms 4,388 KB
testcase_05	AC	1 ms 4,380 KB
testcase_06	AC	2 ms 4,384 KB
testcase_07	AC	1 ms 4,380 KB
testcase_08	AC	2 ms 4,384 KB
testcase_09	AC	2 ms 4,380 KB
testcase_10	AC	1 ms 4,380 KB
testcase_11	AC	2 ms 4,380 KB
testcase_12	AC	2 ms 4,384 KB
testcase_13	AC	2 ms 4,384 KB
testcase_14	AC	1 ms 4,384 KB
testcase_15	AC	4 ms 4,380 KB
testcase_16	AC	4 ms 4,380 KB
testcase_17	AC	4 ms 4,384 KB
testcase_18	AC	4 ms 4,384 KB
testcase_19	AC	4 ms 4,384 KB
testcase_20	AC	4 ms 4,380 KB
testcase_21	AC	2 ms 4,380 KB
testcase_22	AC	5 ms 4,380 KB
testcase_23	AC	4 ms 4,380 KB
testcase_24	AC	234 ms 15,076 KB
testcase_25	AC	235 ms 14,956 KB
testcase_26	AC	238 ms 14,780 KB
testcase_27	AC	240 ms 14,900 KB
testcase_28	AC	234 ms 14,972 KB
testcase_29	AC	236 ms 15,036 KB
testcase_30	AC	249 ms 15,068 KB
testcase_31	AC	234 ms 14,972 KB
testcase_32	AC	1 ms 4,380 KB
testcase_33	MLE	-
testcase_34	--	-
testcase_35	--	-
testcase_36	--	-
testcase_37	--	-
testcase_38	--	-
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <int M>
struct MInt {
  unsigned int v;

  MInt() : v(0) {}
  MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}

  static constexpr int get_mod() { return M; }
  static void set_mod(const int divisor) { assert(divisor == M); }

  static void init(const int x) {
    inv<true>(x);
    fact(x);
    fact_inv(x);
  }

  template <bool MEMOIZES = false>
  static MInt inv(const int n) {
// #if __cplusplus >= 201703L
//     assert(0 <= n && n < M && std::gcd(n, M) == 1);
// #else
//     assert(0 <= n && n < M && std::__gcd(n, M) == 1);
// #endif  // __cplusplus >= 201703L
    static std::vector<MInt> inverse{0, 1};
    const int prev = inverse.size();
    if (n < prev) return inverse[n];
    const auto memoize = [prev, n]() -> void {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[M % i] * (M / i);
      }
    };
#if __cplusplus >= 201703L
    if constexpr (MEMOIZES) {
      memoize();
      return inverse[n];
    }
#else
    if (MEMOIZES) {
      memoize();
      return inverse[n];
    }
#endif  // __cplusplus >= 201703L
    int u = 1, v = 0;
    for (unsigned int a = n, b = M; b;) {
      const unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }

  static MInt fact(const int n) {
    static std::vector<MInt> factorial{1};
    const int prev = factorial.size();
    if (n >= prev) {
      factorial.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        factorial[i] = factorial[i - 1] * i;
      }
    }
    return factorial[n];
  }

  static MInt fact_inv(const int n) {
    static std::vector<MInt> f_inv{1};
    const int prev = f_inv.size();
    if (n >= prev) {
      f_inv.resize(n + 1);
      f_inv[n] = inv(fact(n).v);
      for (int i = n; i > prev; --i) {
        f_inv[i - 1] = f_inv[i] * i;
      }
    }
    return f_inv[n];
  }

  static MInt nCk(const int n, const int k) {
    if (n < 0 || n < k || k < 0) return 0;
    return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
                                  fact_inv(n - k) * fact_inv(k));
  }
  static MInt nPk(const int n, const int k) {
    return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k));
  }

  static MInt large_nCk(long long n, const int k) {
    if (n < 0 || n < k || k < 0) return 0;
    inv<true>(k);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }

  MInt pow(long long exponent) const {
    MInt res = 1, tmp = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }

  MInt& operator+=(const MInt& x) {
    if (static_cast<int>(v += x.v) >= M) v -= M;
    return *this;
  }
  MInt& operator-=(const MInt& x) {
    if (static_cast<int>(v += M - x.v) >= M) v -= M;
    return *this;
  }
  MInt& operator*=(const MInt& x) {
    v = static_cast<unsigned long long>(v) * x.v % M;
    return *this;
  }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }

  bool operator==(const MInt& x) const { return v == x.v; }
  bool operator!=(const MInt& x) const { return v != x.v; }
  bool operator<(const MInt& x) const { return v < x.v; }
  bool operator<=(const MInt& x) const { return v <= x.v; }
  bool operator>(const MInt& x) const { return v > x.v; }
  bool operator>=(const MInt& x) const { return v >= x.v; }

  MInt& operator++() {
    if (static_cast<int>(++v) == M) v = 0;
    return *this;
  }
  MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  MInt& operator--() {
    v = (v == 0 ? M - 1 : v - 1);
    return *this;
  }
  MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }

  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(v ? M - v : 0); }

  MInt operator+(const MInt& x) const { return MInt(*this) += x; }
  MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt& x) const { return MInt(*this) /= x; }

  friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
    return os << x.v;
  }
  friend std::istream& operator>>(std::istream& is, MInt& x) {
    long long v;
    is >> v;
    x = MInt(v);
    return is;
  }
};
using ModInt = MInt<MOD>;

template <int T>
struct NumberTheoreticTransform {
  using ModInt = MInt<T>;

  NumberTheoreticTransform() {
    for (int i = 0; i < 23; ++i) {
      if (primes[i][0] == ModInt::get_mod()) {
        n_max = 1 << primes[i][2];
        root = ModInt(primes[i][1]).pow((primes[i][0] - 1) >> primes[i][2]);
        return;
      }
    }
    assert(false);
  }

  template <typename U>
  std::vector<ModInt> dft(const std::vector<U>& a) {
    const int n = a.size();
    int lg = 1;
    while ((1 << lg) < n) ++lg;
    std::vector<ModInt> b(1 << lg, 0);
    std::copy(a.begin(), a.end(), b.begin());
    calc(&b);
    return b;
  }

  void idft(std::vector<ModInt>* a) {
    const int n = a->size();
    assert(__builtin_popcount(n) == 1);
    calc(a);
    std::reverse(std::next(a->begin()), a->end());
    const ModInt inv_n = ModInt::inv(n);
    for (int i = 0; i < n; ++i) {
      (*a)[i] *= inv_n;
    }
  }

  template <typename U>
  std::vector<ModInt> convolution(const std::vector<U>& a,
                                  const std::vector<U>& b) {
    const int a_size = a.size(), b_size = b.size();
    const int c_size = a_size + b_size - 1;
    int lg = 1;
    while ((1 << lg) < c_size) ++lg;
    const int n = 1 << lg;
    std::vector<ModInt> c(n, 0), d(n, 0);
    std::copy(a.begin(), a.end(), c.begin());
    calc(&c);
    std::copy(b.begin(), b.end(), d.begin());
    calc(&d);
    for (int i = 0; i < n; ++i) {
      c[i] *= d[i];
    }
    idft(&c);
    c.resize(c_size);
    return c;
  }

 private:
  const int primes[23][3]{
    {16957441, 329, 14},
    {17006593, 26, 15},
    {19529729, 770, 17},
    {167772161, 3, 25},
    {469762049, 3, 26},
    {645922817, 3, 23},
    {897581057, 3, 23},
    {924844033, 5, 21},
    {935329793, 3, 22},
    {943718401, 7, 22},
    {950009857, 7, 21},
    {962592769, 7, 21},
    {975175681, 17, 21},
    {976224257, 3, 20},
    {985661441, 3, 22},
    {998244353, 3, 23},
    {1004535809, 3, 21},
    {1007681537, 3, 20},
    {1012924417, 5, 21},
    {1045430273, 3, 20},
    {1051721729, 6, 20},
    {1053818881, 7, 20},
    {1224736769, 3, 24}
  };

  int n_max;
  ModInt root;
  std::vector<int> butterfly{0};
  std::vector<std::vector<ModInt>> omega{{1}};

  void calc(std::vector<ModInt>* a) {
    const int n = a->size(), prev_n = butterfly.size();
    if (n > prev_n) {
      assert(n <= n_max);
      butterfly.resize(n);
      const int prev_lg = omega.size(), lg = __builtin_ctz(n);
      for (int i = 1; i < prev_n; ++i) {
        butterfly[i] <<= lg - prev_lg;
      }
      for (int i = prev_n; i < n; ++i) {
        butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1));
      }
      omega.resize(lg);
      for (int i = prev_lg; i < lg; ++i) {
        omega[i].resize(1 << i);
        const ModInt tmp = root.pow((ModInt::get_mod() - 1) >> (i + 1));
        for (int j = 0; j < (1 << (i - 1)); ++j) {
          omega[i][j << 1] = omega[i - 1][j];
          omega[i][(j << 1) + 1] = omega[i - 1][j] * tmp;
        }
      }
    }
    const int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n);
    for (int i = 0; i < n; ++i) {
      const int j = butterfly[i] >> shift;
      if (i < j) std::swap((*a)[i], (*a)[j]);
    }
    for (int block = 1, den = 0; block < n; block <<= 1, ++den) {
      for (int i = 0; i < n; i += (block << 1)) {
        for (int j = 0; j < block; ++j) {
          const ModInt tmp = (*a)[i + j + block] * omega[den][j];
          (*a)[i + j + block] = (*a)[i + j] - tmp;
          (*a)[i + j] += tmp;
        }
      }
    }
  }
};

template <typename T>
struct FormalPowerSeries {
  std::vector<T> coef;

  explicit FormalPowerSeries(const int deg = 0) : coef(deg + 1, 0) {}
  explicit FormalPowerSeries(const std::vector<T>& coef) : coef(coef) {}
  FormalPowerSeries(const std::initializer_list<T> init)
      : coef(init.begin(), init.end()) {}
  template <typename InputIter>
  explicit FormalPowerSeries(const InputIter first, const InputIter last)
      : coef(first, last) {}

  inline const T& operator[](const int term) const { return coef[term]; }
  inline T& operator[](const int term) { return coef[term]; }

  using Mult = std::function<std::vector<T>(const std::vector<T>&,
                                            const std::vector<T>&)>;
  using Sqrt = std::function<bool(const T&, T*)>;
  static void set_mult(const Mult mult) { get_mult() = mult; }
  static void set_sqrt(const Sqrt sqrt) { get_sqrt() = sqrt; }

  void resize(const int deg) { coef.resize(deg + 1, 0); }
  void shrink() {
    while (coef.size() > 1 && coef.back() == 0) coef.pop_back();
  }
  int degree() const { return static_cast<int>(coef.size()) - 1; }

  FormalPowerSeries& operator=(const std::vector<T>& coef_) {
    coef = coef_;
    return *this;
  }
  FormalPowerSeries& operator=(const FormalPowerSeries& x) = default;

  FormalPowerSeries& operator+=(const FormalPowerSeries& x) {
    const int deg_x = x.degree();
    if (deg_x > degree()) resize(deg_x);
    for (int i = 0; i <= deg_x; ++i) {
      coef[i] += x[i];
    }
    return *this;
  }
  FormalPowerSeries& operator-=(const FormalPowerSeries& x) {
    const int deg_x = x.degree();
    if (deg_x > degree()) resize(deg_x);
    for (int i = 0; i <= deg_x; ++i) {
      coef[i] -= x[i];
    }
    return *this;
  }
  FormalPowerSeries& operator*=(const T x) {
    for (T& e : coef) e *= x;
    return *this;
  }
  FormalPowerSeries& operator*=(const FormalPowerSeries& x) {
    return *this = get_mult()(coef, x.coef);
  }
  FormalPowerSeries& operator/=(const T x) {
    assert(x != 0);
    return *this *= static_cast<T>(1) / x;
  }
  FormalPowerSeries& operator/=(const FormalPowerSeries& x) {
    const int n = degree() - x.degree() + 1;
    if (n <= 0) return *this = FormalPowerSeries();
    const std::vector<T> tmp = get_mult()(
        std::vector<T>(coef.rbegin(), std::next(coef.rbegin(), n)),
        FormalPowerSeries(
            x.coef.rbegin(),
            std::next(x.coef.rbegin(), std::min(x.degree() + 1, n)))
        .inv(n - 1).coef);
    return *this = FormalPowerSeries(std::prev(tmp.rend(), n), tmp.rend());
  }
  FormalPowerSeries& operator%=(const FormalPowerSeries& x) {
    if (x.degree() == 0) return *this = FormalPowerSeries{0};
    *this -= *this / x * x;
    resize(x.degree() - 1);
    return *this;
  }
  FormalPowerSeries& operator<<=(const int n) {
    coef.insert(coef.begin(), n, 0);
    return *this;
  }
  FormalPowerSeries& operator>>=(const int n) {
    if (degree() < n) return *this = FormalPowerSeries();
    coef.erase(coef.begin(), coef.begin() + n);
    return *this;
  }

  bool operator==(FormalPowerSeries x) const {
    x.shrink();
    FormalPowerSeries y = *this;
    y.shrink();
    return x.coef == y.coef;
  }
  bool operator!=(const FormalPowerSeries& x) const { return !(*this == x); }

  FormalPowerSeries operator+() const { return *this; }
  FormalPowerSeries operator-() const {
    FormalPowerSeries res = *this;
    for (T& e : res.coef) e = -e;
    return res;
  }

  FormalPowerSeries operator+(const FormalPowerSeries& x) const {
    return FormalPowerSeries(*this) += x;
  }
  FormalPowerSeries operator-(const FormalPowerSeries& x) const {
    return FormalPowerSeries(*this) -= x;
  }
  FormalPowerSeries operator*(const T x) const {
    return FormalPowerSeries(*this) *= x;
  }
  FormalPowerSeries operator*(const FormalPowerSeries& x) const {
    return FormalPowerSeries(*this) *= x;
  }
  FormalPowerSeries operator/(const T x) const {
    return FormalPowerSeries(*this) /= x;
  }
  FormalPowerSeries operator/(const FormalPowerSeries& x) const {
    return FormalPowerSeries(*this) /= x;
  }
  FormalPowerSeries operator%(const FormalPowerSeries& x) const {
    return FormalPowerSeries(*this) %= x;
  }
  FormalPowerSeries operator<<(const int n) const {
    return FormalPowerSeries(*this) <<= n;
  }
  FormalPowerSeries operator>>(const int n) const {
    return FormalPowerSeries(*this) >>= n;
  }

  T horner(const T x) const {
    T res = 0;
    for (int i = degree(); i >= 0; --i) {
      res = res * x + coef[i];
    }
    return res;
  }

  FormalPowerSeries differential() const {
    const int deg = degree();
    assert(deg >= 0);
    FormalPowerSeries res(std::max(deg - 1, 0));
    for (int i = 1; i <= deg; ++i) {
      res[i - 1] = coef[i] * i;
    }
    return res;
  }

  FormalPowerSeries exp(const int deg) const {
    assert(coef[0] == 0);
    const int n = coef.size();
    const FormalPowerSeries one{1};
    FormalPowerSeries res = one;
    for (int i = 1; i <= deg; i <<= 1) {
      res *= FormalPowerSeries(coef.begin(),
                               std::next(coef.begin(), std::min(n, i << 1)))
             - res.log((i << 1) - 1) + one;
      res.coef.resize(i << 1);
    }
    res.resize(deg);
    return res;
  }
  FormalPowerSeries exp() const { return exp(degree()); }

  FormalPowerSeries inv(const int deg) const {
    assert(coef[0] != 0);
    const int n = coef.size();
    FormalPowerSeries res{static_cast<T>(1) / coef[0]};
    for (int i = 1; i <= deg; i <<= 1) {
      res = res + res - res * res * FormalPowerSeries(
          coef.begin(), std::next(coef.begin(), std::min(n, i << 1)));
      res.coef.resize(i << 1);
    }
    res.resize(deg);
    return res;
  }
  FormalPowerSeries inv() const { return inv(degree()); }

  FormalPowerSeries log(const int deg) const {
    assert(coef[0] == 1);
    FormalPowerSeries integrand = differential() * inv(deg - 1);
    integrand.resize(deg);
    for (int i = deg; i > 0; --i) {
      integrand[i] = integrand[i - 1] / i;
    }
    integrand[0] = 0;
    return integrand;
  }
  FormalPowerSeries log() const { return log(degree()); }

  FormalPowerSeries pow(long long exponent, const int deg) const {
    const int n = coef.size();
    if (exponent == 0) {
      FormalPowerSeries res(deg);
      if (deg != -1) res[0] = 1;
      return res;
    }
    assert(deg >= 0);
    for (int i = 0; i < n; ++i) {
      if (coef[i] == 0) continue;
      if (i > deg / exponent) break;
      const long long shift = exponent * i;
      T tmp = 1, base = coef[i];
      for (long long e = exponent; e > 0; e >>= 1) {
        if (e & 1) tmp *= base;
        base *= base;
      }
      const FormalPowerSeries res = ((*this >> i) / coef[i]).log(deg - shift);
      return ((res * exponent).exp(deg - shift) * tmp) << shift;
    }
    return FormalPowerSeries(deg);
  }
  FormalPowerSeries pow(const long long exponent) const {
    return pow(exponent, degree());
  }

  FormalPowerSeries mod_pow(long long exponent,
                            const FormalPowerSeries& md) const {
    const int deg = md.degree() - 1;
    if (deg < 0) return FormalPowerSeries(-1);
    const FormalPowerSeries inv_rev_md =
        FormalPowerSeries(md.coef.rbegin(), md.coef.rend()).inv();
    const auto mod_mult = [&md, &inv_rev_md, deg](
        FormalPowerSeries* multiplicand, const FormalPowerSeries& multiplier)
        -> void {
      *multiplicand *= multiplier;
      if (deg < multiplicand->degree()) {
        const int n = multiplicand->degree() - deg;
        const FormalPowerSeries quotient =
            FormalPowerSeries(multiplicand->coef.rbegin(),
                              std::next(multiplicand->coef.rbegin(), n))
            * FormalPowerSeries(
                  inv_rev_md.coef.begin(),
                  std::next(inv_rev_md.coef.begin(), std::min(deg + 2, n)));
        *multiplicand -=
            FormalPowerSeries(std::prev(quotient.coef.rend(), n),
                              quotient.coef.rend()) * md;
        multiplicand->resize(deg);
      }
      multiplicand->shrink();
    };
    FormalPowerSeries res{1}, base = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) mod_mult(&res, base);
      mod_mult(&base, base);
    }
    return res;
  }

  FormalPowerSeries sqrt(const int deg) const {
    const int n = coef.size();
    if (coef[0] == 0) {
      for (int i = 1; i < n; ++i) {
        if (coef[i] == 0) continue;
        if (i & 1) return FormalPowerSeries(-1);
        const int shift = i >> 1;
        if (deg < shift) break;
        FormalPowerSeries res = (*this >> i).sqrt(deg - shift);
        if (res.coef.empty()) return FormalPowerSeries(-1);
        res <<= shift;
        res.resize(deg);
        return res;
      }
      return FormalPowerSeries(deg);
    }
    T s;
    if (!get_sqrt()(coef.front(), &s)) return FormalPowerSeries(-1);
    FormalPowerSeries res{s};
    const T half = static_cast<T>(1) / 2;
    for (int i = 1; i <= deg; i <<= 1) {
      res = (FormalPowerSeries(coef.begin(),
                               std::next(coef.begin(), std::min(n, i << 1)))
             * res.inv((i << 1) - 1) + res) * half;
    }
    res.resize(deg);
    return res;
  }
  FormalPowerSeries sqrt() const { return sqrt(degree()); }

  FormalPowerSeries translate(const T c) const {
    const int n = coef.size();
    std::vector<T> fact(n, 1), inv_fact(n, 1);
    for (int i = 1; i < n; ++i) {
      fact[i] = fact[i - 1] * i;
    }
    inv_fact[n - 1] = static_cast<T>(1) / fact[n - 1];
    for (int i = n - 1; i > 0; --i) {
      inv_fact[i - 1] = inv_fact[i] * i;
    }
    std::vector<T> g(n), ex(n);
    for (int i = 0; i < n; ++i) {
      g[i] = coef[i] * fact[i];
    }
    std::reverse(g.begin(), g.end());
    T pow_c = 1;
    for (int i = 0; i < n; ++i) {
      ex[i] = pow_c * inv_fact[i];
      pow_c *= c;
    }
    const std::vector<T> conv = get_mult()(g, ex);
    FormalPowerSeries res(n - 1);
    for (int i = 0; i < n; ++i) {
      res[i] = conv[n - 1 - i] * inv_fact[i];
    }
    return res;
  }

 private:
  static Mult& get_mult() {
    static Mult mult = [](const std::vector<T>& a, const std::vector<T>& b)
        -> std::vector<T> {
      const int n = a.size(), m = b.size();
      std::vector<T> res(n + m - 1, 0);
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
          res[i + j] += a[i] * b[j];
        }
      }
      return res;
    };
    return mult;
  }
  static Sqrt& get_sqrt() {
    static Sqrt sqrt = [](const T&, T*) -> bool { return false; };
    return sqrt;
  }
};

tuple<int, int, int> sort(const int a, const int b, const int c) {
  int abc[]{a, b, c};
  sort(abc, abc + 3);
  return {abc[0], abc[1], abc[2]};
}

// https://yukicoder.me/problems/no/2013
int main() {
  FormalPowerSeries<ModInt>::set_mult([](const vector<ModInt>& a, const vector<ModInt>& b) -> vector<ModInt> {
    static NumberTheoreticTransform<MOD> ntt;
    return ntt.convolution(a, b);
  });

  int n, x1, y1, x2, y2, A, B; cin >> n >> x1 >> y1 >> x2 >> y2 >> A >> B;
  x2 = abs(x2 - x1);
  y2 = abs(y2 - y1);
  if ((x2 + y2) % 2 == 1) {
    cout << 0 << '\n';
    return 0;
  }
  vector<int> a(n); REP(i, n) cin >> a[i];
  const ModInt al = ModInt::inv(2) * A / (A + B), be = ModInt::inv(2) * B / (A + B);

  FormalPowerSeries<ModInt> qx(n), qy(n);
  REP(i, n + 1) qx[i] = al.pow(x2 + i * 2) * ModInt::fact_inv(x2 + i) * ModInt::fact_inv(i);
  REP(i, n + 1) qy[i] = be.pow(y2 + i * 2) * ModInt::fact_inv(y2 + i) * ModInt::fact_inv(i);
  qx *= qy;
  FormalPowerSeries<ModInt> q(n);
  for (int i = x2 + y2; i <= n * 2; i += 2) {
    q[i / 2] = qx[(i - x2 - y2) / 2] * ModInt::fact(i);
  }
  // REP(i, n + 1) cout << q[i] << " \n"[i == n];

  FormalPowerSeries<ModInt> sx(n), sy(n);
  REP(i, n + 1) sx[i] = al.pow(i * 2) * ModInt::fact_inv(i) * ModInt::fact_inv(i);
  REP(i, n + 1) sy[i] = be.pow(i * 2) * ModInt::fact_inv(i) * ModInt::fact_inv(i);
  sx *= sy;
  FormalPowerSeries<ModInt> s(n);
  for (int i = 0; i <= n * 2; i += 2) {
    s[i / 2] = sx[i / 2] * ModInt::fact(i);
  }

  q *= s.inv();
  ModInt ans = 0;
  FOR(i, 1, n + 1) ans += q[i] * a[i - 1];
  cout << ans << '\n';
  return 0;
}